Packing identical spheres into a cylinder

The paper deals with the optimization problem of packing identical spheres into a cylinder of minimal height. A mathematical model of the problem is constructed and its characteristics are considered. On the ground of characteristics, a strategy of searching for an approximation to a global minimum is offered. The strategy includes a special search tree construction, a modification of the Zoutendijk method of feasible directions to calculate local minima, and a modification of the decremental neighborhood method to search for an approximation to a global minimum. Numerical examples and performance analysis of solutions are given. On the basis of the mathematical model and numerical experiment, a number of conclusions are drawn.